ThmDex – An index of mathematical definitions, results, and conjectures.
Formulation F13267 on D4115: Gram-Schmidt projection
F13267
Formulation 1
Let $I$ be an D1128: Inner product space such that
(i) $\langle \cdot, \cdot \rangle$ is the D34: Inner product on $I$
(ii) $x, y \in I$ are each a D1129: Vector in $I$
(iii) \begin{equation} y \neq 0_I \end{equation}
The Gram-Schmidt projection for $(x, y)$ in $I$ is the D1129: Vector \begin{equation} \frac{\langle x, y \rangle}{\langle y, y \rangle} y \end{equation}